I've usually heard shone and scone to rhyme with on. Scone with a long o denotes someone who has been to Britain recently and shone is a bit high-falutin for the colonies. (except when someone is shown the door) But then I gave up on expecting English to follow its own rules long ago.
It is very important, when buying a foreign phrase book to get one written in your own neighbourhood or all the little pronunciation tips turn into slips. eg the Berlitz book that made a distinction between the "oo" sound in school and the "u" sound in tube. In Canada (Western anyway) they are identical to that in roof. There is no Canadian equivilant that I can think of to the American vowel in roof.